Abstract: Face space is the low dimensional manifold embedded in high dimensional observation space.To describe the convex and bow structure of the manifold，a novel face recognition algorithm coined 2D geodesic preserving projection is proposed.Matrix is explored to represent face image.Based on the matrix-representation model，2D geodesic preserving projection algorithm is employed to compute the low dimensional embedded manifold.Projection on the manifold of face image is utilized as the feature for face recognition.Experimental results on CMU PIE database verify the effectiveness of the proposed algorithm.

Key words: face recognition, Geodesic Preserving Projection（GPP）, manifold learning

摘要： 人脸空间是嵌套在高维观测空间中的低维流形，为了更好地描述人脸空间的凸起和凹进等细微结构，提出了一种基于二维测地线距离保持映射的人脸识别算法。算法采用矩阵的模式表示人脸空间中的样本图像；基于图像的矩阵表示模型，采用二维测地线距离保持映射算法计算人脸空间的低维嵌套流形；以人脸样本在低维流形空间中的投影为特征进行人脸识别。在CMU PIE人脸数据库上的实验结果验证了算法的合理性和有效性。

关键词: 人脸识别, 测地线距离保持映射, 流形学习